Express this quotient in scientific notation: ${\frac{1.170\times 10^{7}} {9.0\times 10^{2}}}$
Solution: Start by collecting like terms together. $= {\frac{1.170} {9.0}} \times{\frac{10^{7}} {10^{2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.13 \times 10^{7\,-\,2}$ $= 0.13 \times 10^{5}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.13$ is the same as $1.30 \div 10$ , or $1.30 \times 10^{-1}$ $ = {1.30 \times 10^{-1}} \times 10^{5} $ $= 1.30\times 10^{4}$